\(L^2\)-error analysis of discontinuous Galerkin approximations for nonlinear Sobolev equations (Q1943088)

The authors apply a discontinuous Galerkin method with symmetric interior penalty terms to approximate the solution of nonlinear Sobolev equations. They introduce an appropriate elliptic type projection of the solution of a Sobolev equation and prove its optimal convergence. Finally, a semidiscrete approximation of the solutions of nonlinear Sobolev differential equations is constructed, and their convergence in \(L^2\) normed space with optimal order of convergence is proved.